Student guide
1. Design a flower
Every flower here is built the same way: the full turn around the center, 360°, is shared equally by the petals. With 6 petals each gets 360 ÷ 6 = 60°. With 100 petals each gets only 3.6°, so the petals are thin, like a daisy or a sunflower.
Petal i points along angle 360°·i/n, and each petal is drawn inside its own wedge of width 360°/n, so the petals touch only at the center. The tips are the vertices of a regular n-gon inscribed in the circle of radius R, with side 2R sin(180°/n) and interior angle 180°(n−2)/n.
Star polygons
Join every second tip of a 6-petal flower and you get two triangles that make a six-pointed star. With 5 petals, joining every second tip draws a five-pointed star in one line without lifting your pencil.
The star polygon {n/k} joins every k-th tip. It breaks into gcd(n, k) separate pieces, each a {(n/d)/(k/d)} figure. So {6/2} is two triangles, {12/4} is four triangles, and {8/3} is one star traced in a single path. Each point of a single star has angle 180°(n−2k)/n.